Question: Let f be integrable on [-, ] and L R. a) Prove that if {N f)(x0) L as N and if (Sf)(x0)

Let f be integrable on [-Ï€, Ï€] and L ˆˆ R.
a) Prove that if {σN f)(x0) L as N †’ ˆž and if (Sf)(x0) converges, then (SNf)(x0)) †’ L.
b) Prove that
Let f be integrable on [-Ï€, Ï€] and L ˆˆ

converges to ˆš2Ï€ cos ˆš2x uniformly on compact subsets of (0, 2Ï€).

1)" sin V2 2_k2 .cos kx. ]

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